Figure 5

Empirical and theoretical h -index distribution. (a) Testing the predictions of a stochastic h-index model with empirical data. Shown for each dataset is the empirical probability density function $P(h)$, using logarithmic binning for $h>10$. We fit each $P(h)$ to the model distribution $P_m(h)$, parametrized by only the distribution average, which is related to the mixing model parameters as $〈h〉={\lambda }_1{\lambda }_2$. (Inset) Data collapse of the empirical distributions along the universal curve $K_0(\sqrt{h};{\lambda }_1{\lambda }_2=1)$ (dashed grey curve) using the scaled variable $x=h/〈h〉$. (b) 6,498,286 clusters with $h\ge 2$ were identified for the entire WoS disambiguation. Plotted are the probability distribution $P(h)$ (green circles), the best-fit model $P_m(h)$ with ${\lambda }_1{\lambda }_2=3.49$, and the complementary cumulative distribution $P(\ge h)$ (solid black curve). The numbers indicate the value associated with the percentile $100\times (1-P(h))$, e.g. 1 per 1,000 clusters (corresponding to the 99.9th percentile) has h-index of 64 or greater.